Influenza transmissibility among patients and health-care professionals in a geriatric short-stay unit using individual contact data

Detailed information are lacking on influenza transmissibility in hospital although clusters are regularly reported. In this pilot study, our goal was to estimate the transmission rate of H3N2 2012-influenza, among patients and health care professionals in a short-term Acute Care for the Elderly Unit by using a stochastic approach and a simple susceptible-exposed-infectious-removed model. Transmission parameters were derived from documented individual contact data collected by Radio Frequency IDentification technology at the epidemic peak. From our model, nurses appeared to transmit infection to a patient more frequently with a transmission rate of 1.04 per day on average compared to 0.38 from medical doctors. This transmission rate was 0.34 between nurses. These results, even obtained in this specific context, might give a relevant insight of the influenza dynamics in hospitals and will help to improve and to target control measures for preventing nosocomial transmission of influenza. The investigation of nosocomial transmission of SARS-COV-2 might gain from similar approaches.


Determination of the matrix multiplicative factor ( )
The average duration of Hospital Care Professional (HCP) contacts are extremely short in our data compared with those reported in the literature. We observed indeed a mean duration of 0.77 min (46 s) ranging from 0.33 to 12 min and a median of 0.33 [IQR, 0.33-1.0] min. But, in a study dealing with HCP exposure to tuberculosis infected patients 1 , the average duration of a HCP visit manually recorded in a patient room was 3 min 26s ranging from 10 s to 18 min i.e. 4.5 times higher than our results on average.
In another paper of the same previous team, the median interaction duration between HCP and patients was 2.5 [IQR, 1.6-7.7] min by radiofrequency identification 2 i.e. from 6 to 7.6 times higher than our median duration. Contacts within 1 meter were recorded in our study whereas the maximal distance was from 1.5 to 2.74 m (9 feet) in other studies 1,3-6 , i.e. almost 3 times farther. Furthermore, face-toface contact means that two persons sitting next to each other who talk might not be recorded as a contact. Consequently, a ward assistant busy in a patient room for a while might not be recorded at all in our data.
To counteract these drawbacks, we computed the average relative error of prediction of our model by varying the multiplicative factor ( ) between 1 and 10 step 1. The transmission matrix ( ) was estimated with all susceptibility and infectivity parameters set to the default value 1, the latency period was fixed at 0.5 day and the infectious period varied from 1 to 4 step 1 for patients and HCP. This led to test 80 parameter combinations (scenarios) i.e. 10 × 2 × 4. For each scenario, 2,000 simulations were performed using the stochastic SEIR model. The mean of the predicted number of incident cases by subject category (patient, nurse, medical doctors) was computed over the 2,000 simulations for each scenario. The mean prediction error for a given scenario was the average over the subject category of the absolute difference between the numbers of observed and mean predicted incidence cases. The relative error (RE) of prediction per scenario was then computed as follows: with denoting population (1: patients; 2: nurses; 3: medical doctors); the Observed number of incident cases in population during the 10-days study period and the average of the Predicted Number of incident cases in population for the simulation over all 2,000 simulations.
The average relative error of prediction per multiplicative factor is reported in Fig. 1 below.

Evaluation of the susceptibility of patients faced to contagious patients
In Vanhems et al. 7  Then, we considered that patient infectivity towards susceptible patients might be 3-fold the HCW infectivity toward susceptible patients. The patient infectivity toward susceptible patients denoted by 11 parameter therefore varied between 1 and 3.

Duration of the contacts between two individuals
Contact duration ranged from 20 seconds to almost 1 hour 51 minutes. The longest contact duration was between two interns (residency program) who were on ward duty by night. Over the 17,947 contacts, 99.1% (17,791) of them lasted no more than 5 minutes. Supplementary Fig.2 gives the distribution of their duration.

Estimation of the next generation matrix at the beginning of the study
We estimated the next generation matrix according to Diekmann et al. 8,9 . We computed then the mean for each matrix element.
Nurses appeared to be involved in patient infection. The mean reproduction number from an infectious nurse toward susceptible patients ( 12 ) was the largest among the 9 possible reproduction numbers ( Supplementary Fig. 3).
Supplementary Figure 3. Effective reproduction number matrix obtained on average for the 84 best scenarios with relative error less than 5%. 7

Underlying differential equations system
The transition rates (see Table 3 in the main text) were deduced from the following ordinary differential equations that describe the dynamics of the diagram of the transitions between the states given in Fig. 2 in the main text. anonymous timetable corresponding to the same period study.
8 With the number of hospitalized patients in the ward ( = 1) or the total number of HCP ( ∈ {2,3}).
The initial conditions were taken as follows: 6 individuals (3 PAT, 1 NUR and 2 MD) were prevalent contagious cases at the beginning of the study period.
In the model, the population of patients at time corresponds to patients hospitalized in the ward at time and the populations of HCP (nurses and medical doctors) correspond to HCP assigned to the ward during the study period.
An average fixed number of 1 patients could enter the ward per day into two possible states, susceptible or contagious, with probability (1 − ) and respectively. A number of 1 patients left the ward per day in any of the 4 possible states (Susceptible/Exposed/Infectious/Removed) with the same probability. The HCP populations were closed assuming no-change in the staff team during the short study period.
We did not take the transmission of influenza in the community into account because of the short stay of patients in the ward. Indeed, we assumed the cautiousness of the families when visiting elderly individuals.